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Miscellaneous Exercise 8 (II) · Q43
Q.

Given below is the frequency distribution of marks obtained by 100 students. Compute arithmetic mean and S.D.

Marks40-4950-5960-6970-7980-8990-99
No. of students4122528265
Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
78% · 43/55 Questions
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Step 1: Mid-values of the classes 40-49,...,90-99 are 44.5, 54.5, 64.5, 74.5, 84.5, 94.5, with N=∑fi=4+12+25+28+26+5=100N=\sum f_i=4+12+25+28+26+5=100.

Step 2: ∑fixi=178+654+1612.5+2086+2197+472.5=7200\sum f_ix_i = 178+654+1612.5+2086+2197+472.5=7200, so xˉ=7200/100=72\bar{x}=7200/100=72.

Step 3: ∑fixi2=7921+35643+104006.25+155407+185646.5+44651.25=533275\sum f_ix_i^2 = 7921+35643+104006.25+155407+185646.5+44651.25=533275. …

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